A collection is whatever stands to a general predicate of single subjects in a certain relation sui generis, such that for every such predicate there is a single collection and for every collection there is such a predicate.

Mathematics is a study of exact hypotheses, in so far as consequences can be deduced from them. To limit mathematics to the deduction of those consequences would be to separate from it some of the greatest of the achievements of modern mathematicians, – achievements which nobody but mathematicians could have performed, – such as the formation of the idea of the system of imaginaries, and of the idea of Riemann surfaces. It must be allowed, therefore, that the formation of the hypotheses is a part of the business of mathematics.